Mock Eisenstein series associated to partition ranks

This talk concerns joint work with Kathrin Bringmann and Jan-Willem van Ittersum. We introduce a new class of mock Eisenstein series that resemble classical Eisenstein series in many ways, but with a key distinction: only their non-holomorphic completions transform like (quasi)modular forms. We show how the partition rank generating function can be expressed in terms of partition traces of these functions. A key feature of our construction is that the completions satisfy a holomorphic anomaly equation--a phenomenon typically seen in the context of quantum field theory and string theory. We also show that the Fourier coefficients of the mock Eisenstein series are integral.